Visualizing the interplay of electron correlations, topology and magnetism

Modern technology, from smartphones to particle accelerators, is rooted in the discovery of new materials with unique properties, such as semiconductors for computing devices and superconductors for medical magnetic resonance imaging. Many of these transformative technologies originate from the exotic properties of quantum materials (QMs). To design QMs with desirable properties, it is essential to understand their microscopic mechanisms. Exotic properties and new states of matter emerge from the collective and organized behaviour of electrons. Consequently a widespread endeavour is underway to deepen our understanding of emergent quantum states. The study of topology, magnetism and strongly correlated electrons were initially separate fields. Until recently, the integration of these three fields has revealed exciting potential for physics. A promising way to achieve correlated topology is to identify QMs with geometrically frustrated structure. The kagome lattice inhibits the free movement of electrons, enhancing the electron-electron interaction and leading to diverse quantum phenomena: electron correlations lead to unconventional charge orders, Dirac fermions lead to topological states of matter, and local magnetism is putatively induced by loop currents. This lattice connects atomic structure with quantum phenomena, advancing our ability to create materials with desired quantum properties. The tunability of kagome materials (KAMs) adds another dimension to control the spin-orbit properties and electronic states. Now the investigation of KAMs has become an exciting frontier of condensed matter physics, filled with opportunities but confronted with significant challenges: the order parameters of quantum states are undefined, their responses to external excitations are unclear, and the nature of loop currents in unknown. Current scanning tunnelling microscopy (STM) research on KAMs is limited by studies at 4 K (low energy resolution), using metallic tips (failed to detect subtle electronic states), and employing uniaxial magnetic fields (no influence topological states). To address these challenges, my proposed research will focus on exploring KAMs employing beyond state-of-the-art STM techniques under extreme conditions. My STM features millikelvin temperatures to achieve ultrahigh energy resolution, vector magnetic fields to manipulate topological states, and tips integrated with optical fibre to investigate dynamics. I will apply fields, light and heat to tune the quantum states and simultaneously measure their order parameter to understand their dynamics. My technique's exceptional precision and speciality provide unprecedented detailed observation of unconventional charge orders, topological bands and loop currents. I will study three representative classes of KAM including the kagome metal AV3Sb5, the Weyl semimetals Co3Sn2S2 and the Chern magnets RMn6Sn6. This project, rooted in recent developments in correlated electron systems, new topological materials and STM technology, positions my work at the cutting edge of physics, representing an overarching convergence of modern techniques and concepts. This project focuses on atomic-scale visualization and control of quantum mechanics. Gaining insight into the microscopic mechanisms paves the way for connecting the quantum states at the atomic-scale to emergent novel properties and for engineering materials by design. I will guide material synthesizers on the impact of atomic-scale inhomogeneities on electronic structures and advise on refining edge structures to improve the stability of topological states. The spin-orbit coupling make KAMs promising materials platform for developing scalable devices in spintronics. The topologically protected states make the kagome magnet an ideal candidate for topologically protected quantum memory in quantum information. The quantum effects to be uncovered may underpin future technologies in the latter half of this century.